Let a be a given positive real number and let W be the open wedge-shapeddomain, defined using polar-coordinates as follows:
W := { (r, θ) | 0 ≤ r < a, 0 < θ < π/3}
a) Use the method of separation of variables to solve the following boundary-value problem for Laplace's equation:

Δu(r,θ) = 0, (r,θ) W,
u(a,θ) = 2sin(6θ), 0 ≤ θ ≤ π/3,
u(r,0) = 0, 0 ≤ r ≤ a,
u(r,π/3) = 0, 0 ≤ r ≤ a.

Note: In polar coordinates, one that Δu = uᵣᵣ + 1/ruᵣ + 1/r²uθθ, whenever r > 0